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# Frequency Distributions and Graphs

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Learn how to organize and present data using frequency distribution and graphs.

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### Frequency Distributions and Graphs

1. 1. BeOrganized
2. 2. How do wepresent the results of a study?
3. 3. Textual Form Tabular Form
4. 4. Graphical Form Horizontal Bar Graph Vertical Bar Graph Multiple Bar Graph
5. 5. Graphical Form Line Graph Pie Graph Picture Graph
6. 6. Let’s say you asked your classmates’ score in your 1st Geometry TestRAW DATA How do you organize the raw data?
7. 7. Frequency Distributionis the organization of raw data intable form, using class intervals andfrequencies Class Interval is the range into which data are divided Frequency (f) number of data values that fall in the range
8. 8. How do you construct a frequencydistribution table?
9. 9. 1. Identify the highest value (HV) and the lowest value (LV).2. Calculate the range: R = HV – LV R = 100 – 70 = 30
10. 10. 3. Find the number of class intervals, using Sturge’s formula: K = 1 + 3.3 log N K = number of class intervals N = total number of observations K = 1 + 3.3 log 50 K = 6.61 K = 7 (rounded to the nearest whole number)
11. 11. 4. Determine the class width. Class width = R (number of data) K Class width = 30 = 4.28 7 Class width = 5 (next whole number)5. The beginning of the 1st class interval (lower class limit) should be near the lowest value and be a multiple of the class width.
12. 12. lower class limit upper class limit70 – 74 (70,71,72,73,74)75 – 79 Tip: lower class limit80 – 84 should be a multiple of the class width85 – 8990 – 94 Class limits do not overlap.95 – 99100 – 104
13. 13. 7. Obtain the class boundaries.Subtract 0.5 from each lower classlimits and add 0.5 to each upper limits. 70 – 74 69.5 – 74.5 75 – 79 74.5 – 79.5 80 – 84 79.5 – 84.5 85 – 89 84.5 – 89.5 90 – 94 89.5 – 94.5 95 – 99 94.5 – 99.5 100 – 104 99.5 – 104.5
14. 14. 8. Find the midpoint or class mark of each class interval.Class mark = lower limit + upper limit 2 70 – 74 72 75 – 79 77 Class marks 80 – 84 82 also follow the 85 – 89 87 class width. 90 – 94 92 95 – 99 97 100 – 104 102
15. 15. 9. Tally the raw scores and indicate the frequency for each class intervals. Or…=COUNTIF(dataset,”x”)=COUNTIF(dataset,”x1”)+COUNTIF(dataset,”x2”) =COUNTIF(C3:G12,”70”)+COUNTIF(C3:G12,”71”)+...
16. 16. 9. Tally the raw scores and indicate the frequency for each class intervals. Count the highlighted cells. Highlight the data set.
17. 17. Frequency Distribution Table
18. 18. Task 2 (save file as T1A2_section_surname)a. The same file (Frequency Distribution.xlsx) contain Sheets 2 and 3.b. Construct frequency distribution tables for the data sets found in Sheets 2 and 3. Note: For sheet 3, the data values contain a decimal point. The class width should be rounded off to the higher value using the same number of decimal place as the given data. To get the class boundaries ±0.05 is used.
19. 19. What are thedifferent types of frequency distributions?
20. 20. Relative Frequency DistributionIt indicates how many percent of the data fall within each category. Pf = class frequency x 100% total frequency =8/50 =8/50*100 or or =cell/50 =cell*100
21. 21. Cumulative Frequency DistributionIt shows the accumulation of the frequencies of the class intervals or categories of data. Less than cumulative frequency (Cf <) Greater than cumulative frequency (Cf >) =42-8 =34-5 =16+5 =21+11
22. 22. Task 2 (continuation)c. Construct relative frequency distributions and cumulative frequency distributions for the data sets found in Sheets 2 and 3. Note: Save file as T1A2_section_surname in your folder located in drive D.
23. 23. How do you graphicallyrepresent the frequency distribution table?
24. 24. HistogramIt shows vertical bars representing class intervals or categories on a frequency distribution. You can change the properties of the table. Highlight the columns.
25. 25. You can change the color of the bars.Double click on a bar and it will show formatting options. You can also show boundaries to the bars.
26. 26. Frequency PolygonIt is constructed by plotting the frequencies against the corresponding class marks, connecting successive points by means of straight lines. Create class marks beyond the class intervals
27. 27. Minimum: extra class mark Maximum: extra class mark Major unit: class widthDouble click the values alongthe x-axis to format the graph.
28. 28. Task 2 (continuation)d. Construct histograms and frequency polygons for the data sets found in Sheets 2 and 3. Note: Save file as T1A2_section_surname in your folder located in drive D.
29. 29. Cumulative Frequency Curve or OgiveIt can be used in estimating the number of cases falling below a given value within the range distribution. Identify lower class boundaries and add extra LCBs
30. 30. Minimum: extra lower class boundaryMaximum: extra lower class boundaryMajor unit: class width
31. 31. Task 2 (continuation)d. Construct cumulative frequency curve for the data sets found in Sheets 2 and 3. Note: Save file as T1A2_section_surname in your folder located in drive D.